Submerged Funicular Arches
Publication: Journal of Structural Engineering
Volume 126, Issue 5
Abstract
This paper evaluates momentless, or funicular, arches designed using Bernoulli-Euler beam theory and evaluates the errors associated with the Bernoulli-Euler and straight-beam approximations. When arches support hydrostatic pressure imposed by water of finite depth, the funicular arch shape depends on the ratio of the water depth to the arch height. Shallow momentless arches [in which the arch height is less than (1/10) the arch span] under deep water (where the water depth is greater than 10 times the arch height) are nearly parabolic in shape. On the other hand, tall momentless arches [in which the arch height is almost (1/2) the arch span] under deep water are nearly semicircular in shape. Momentless arches of intermediate aspect ratios are neither semicircular nor parabolic. The error arising from using straight beam theory (for the bending stresses only) is less than 5% for ratios of beam-depth to radius of curvature less than (1/2). Analyses including bending, shear, and axial deformations and hydrostatic pressure applied to the outer surface of the arch show that the internal moments can reach 10% of the moments of a straight beam of equal span, depending on the thickness and shape of the arch.
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References
1.
Amazigo, J. C. (1978). “Optimal shape of shallow circular arches against snap-buckling.” J. Appl. Mech., 45(9), 591–594.
2.
Ang, B. W., Teo, K. L., and Wang, C. M. (1988). “Optimal shape of arches under bending and axial compression.”J. Engrg. Mech., ASCE, 114(5), 898–905.
3.
Billington, D. P. (1977). “History of esthetics in concrete arch bridges.”J. Struct. Div., ASCE, 103(11), 2129–2143.
4.
Budiansky, B., Frauenthal, J. C., and Hutchinson, J. W. (1969). “On optimal arches.” J. Appl. Mech., 36(12), 880–882.
5.
Farshad, M. (1976). “On optimal form of arches.” J. Franklin Inst., 302(2), 187–194.
6.
Lim, C. W., Wang, C. M., and Kitipornchai, S. (1997). “Timoshenko curved beam bending solutions in terms of Euler-Bernoulli solutions.” Archive of Appl. Mech., 67(2), 179–190.
7.
Rozvany, G. I. N., and Wang, C.-M. (1983). “On plane Prager-structures—I.” Int. J. Mech. Sci., 25(7), 519–527.
8.
Serra, M. (1994). “Optimal arch: Approximate analytical and numerical solutions.” Comp. and Struct., 52(6), 1213–1220.
9.
Stadler, W. (1977). “Natural structural shapes of shallow arches.” J. Appl. Mech., 44(6), 291–298.
10.
Tadjbakhsh, I. G. (1981). “Stability and optimum design of arch-type structures.” Int. J. Solids Struct., 17(6), 565–574.
11.
Vanderplaats, G. N., and Han, S. H. (1990). “Arch shape optimization using force approximation methods.” Struct. Optimization, 2(4), 193–201.
12.
Whitney, C. S. (1925). “Design of symmetrical concrete arches.” Trans. ASCE, 88, 931–1029.
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Received: Jan 20, 1999
Published online: May 1, 2000
Published in print: May 2000
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